# Worksheet: Distribution of Molecular Speeds

In this worksheet, we will practice calculating the proportion of particles, in an ideal gas, that have a given speed using the Maxwell–Boltzmann distribution function.

Q1:

An incandescent light bulb is filled with neon gas. The gas that is in close proximity to the element of the bulb is at a temperature of 2,300 K. Determine the root-mean-square speed of neon atoms in close proximity to the element. Use a value of 20.2 g/mol for the molar mass of neon.

• A m/s
• B m/s
• C m/s
• D m/s
• E m/s

Q2:

Helium atoms in a gas that is at a temperature have a root-mean-square speed of 196 m/s. When the gas is heated until it becomes a plasma with a temperature , the root-mean-square speed of the helium atoms is 618 km/s. Use a value of 4.003 g/mol for the molar mass of helium.

Find .

Find .

• A K
• B K
• C K
• D K
• E K

Q3:

Using the approximation for small , estimate the fraction of nitrogen molecules at a temperature of K that have speeds between 290 m/s and 291 m/s. A nitrogen molecule has a mass of kg.

Q4:

Find the ratio for hydrogen gas at a temperature of 77.0 K. Use a molar mass of 2.02 g/mol for hydrogen gas.

Q5:

In a sample of a monatomic gas, a number of molecules have speeds that are within a very small range around the root-mean-square speed of atoms in the gas, . A number of molecules have speeds that are within the same very small range around a speed of . Determine the ratio of to .

Q6:

A sample of nitrogen is at a temperature of 3,015 K. has a molar mass of 28.00 g/mol.

What is the most probable speed of the nitrogen molecules?

What is the average speed of the nitrogen molecules?

What is the root-mean-square speed of the nitrogen molecules?